L-FNO: Lorentzian Fourier Neural Operator for Stochastic Event Dynamics

Abstract:Modern operational systems face uncertainty even in routine conditions, where rare, bursty, and self-exciting events emerge from both exogenous covariates and endogenous event dynamics. Standard neural operators are typically trained as regression-style function-to-function models rather than conditional-intensity estimators, limiting their suitability for sparse event regimes. We introduce the Lorentzian Fourier Neural Operator (L-FNO), a stochastic neural operator that combines an FNO-style covariate path, Lorentzian spectral kernels for history-dependent excitation, and a likelihood-based training objective. We evaluate L-FNO on eight synthetic point-process benchmarks and three real-world datasets covering disease outbreak prediction and semiconductor fault or defect detection. L-FNO improves event likelihood, calibration diagnostics, and rare-event detection over regression- and likelihood-based neural operator baselines. These results show that structured spectral memory and likelihood-based learning provide effective inductive biases for neural operator models of stochastic event dynamics.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2608.13562 [cs.LG]

(or arXiv:2608.13562v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.13562 Focus to learn more arXiv-issued DOI via DataCite

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